The applicant of the present application previously disclosed 10-(3-cyclopropylaminomethyl-4-fluoropyrrolidinyl)pyridobenzoxazine carboxylic acid derivatives as antimicrobial agents that are safe and effective against drug-resistant bacteria (Patent Document 1). This patent document describes a production process of 3-cyclopropylaminomethyl-4-fluoropyrrolidine that serves as a useful intermediate. Nonetheless, the process still had drawbacks that need to be addressed to make it ideal for mass-production and industrial use. The applicant later disclosed an improved process for synthesizing (3R,4S)-3-cyclopropylaminomethyl-4-fluoropyrrolidine (Patent Document 2). The process described in Patent Document 2 uses (3R,4R)-(1-benzyloxycarbonyl-4-hydroxypyrrolidine-3-yl)methanol as a starting material. In this process, the primary hydroxyl groups are first brominated and the secondary hydroxyl groups are subsequently fluorinated. The resulting product is then reacted with a cyclopropylamine derivative. Subsequent removal of the benzyloxycarbonyl protecting group gives the target product. Since all of the intermediates produced in this process are oil-like materials, the process requires frequent purification by silica gel column to purify these products. In addition, the introduction of the cyclopropylamine derivative requires an excess amount of cyclopropylamine and heating in an autoclave. Thus, the process is not favorable in terms of workability and cost and it has been difficult to implement this process on an industrial scale. In order to address these problems, there is a need to develop a production process suitable for practical production of the intermediate.    Patent Document 1: WO03/078439 pamphlet    Patent Document 2: Japanese Patent Application Laid-Open No. 2005-239617